$A B C$ is an isosceles triangle with an inscribed circle with centre $O$. Let $P$ be the midpoint of $B C$. If $A B=A C=15$ and $B C=10$, then $\mathrm{OP}$ equals

Question

$A B C$ is an isosceles triangle with an inscribed circle with centre $O$. Let $P$ be the midpoint of $B C$. If $A B=A C=15$ and $B C=10$, then $\mathrm{OP}$ equals, $\frac{\sqrt{5}}{\sqrt{2}}$ unit, $\frac{5}{\sqrt{2}}$ unit, $2 \sqrt{5}$ unit, $5 \sqrt{2}$ unit

MARKS App · Accepted Answer

Hint : $\begin{aligned} & A P=\sqrt{15^2-5^2}=10 \sqrt{2} \ & \Delta=\frac{1}{2} \cdot B C \cdot A P=50 \sqrt{2} \ & s=\frac{15+15+10}{2}=20 \ & \because r=\frac{\Delta}{s}=\frac{50 \sqrt{2}}{20}=\frac{5}{\sqrt{2}}\end{aligned}$

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